Creatine kinase system050920.md

Creatine kinase system¹

$$ \begin{aligned} V_{CK} =C_{CK}*(V_{f}\frac{ATP\cdotp Cr}{K_{ia} K_{B}} -V_{b}\frac{ADP\cdotp PCr}{K_{ic} K_{d}} )/DEN_{CK} \\ DEN_{CK} =1+\frac{Cr}{K_{ib}} +\frac{PCr}{K_{id}} +ATP(\frac{1}{K_{ia}} +\frac{Cr}{K_{ia} K_{b}} )+ADP(\frac{1}{K_{ic}} +\frac{PCr}{K_{id} K_{c}} +\frac{Cr}{K_{ic} K_{Ib}} )\\ J_{syn} =V_{ATPase} \\ J_{diff,ATP} =R_{ATP}( \frac{ATP_{ims}}{V_{ims}}\ -ATP{cyt})\\ J_{diff,ADP} =R_{ADP}( ADP_{ims} -ADP)\\ J_{diff,PCr} =R_{PCr}( PCr_{ims} -PCr) \\ J_{diff,Cr} =R_{Cr}( Cr_{ims} -Cr) \\ J_{diff,Pi} =R_{Pi}( Pi_{ims} -Pi) \\ \end{aligned} $$

$$ \begin{aligned} J_{hyd} =H_{ATP(max)} \ 6t/t_{cycle} \ \ \ \ \ for\ \ \ \ \ 0< t< 1/6 t_{cycle} \

J_{hyd} =H_{ATP(max)} \ [1-6(t/t_{cycle} -1/6)]\ \ \ \ \ for\ \ \ \ \ 1/6\ t_{cycle} < t< 1/3 t_{cycle} \

J_{hyd} =0\ \ \ \ \ for\ \ \ \ \ 1/3 t_{cycle} < t< t_{cycle} \ \end{aligned} $$

Parameter	Value	Units	Desc.
MiCK			mitochondrial creatine kinase enzyme
$V_{max,Mi,f}$	2.658E-3	mM/ms	maximum velocity in the forward direction (PCr production)
$V_{max,Mi,b}$	calculated	mM/ms	maximum velocity in the backward direction (ATP production); Vb/Vf = 4.199
$K_{ia, Mi}$	7.1532E-1	mM	binary dissociation constant ATP
$K_{ib, Mi}$	2.8733E1	mM	binary dissociation constant Cr
$K_{ic, Mi}$	2.017E-1	mM	binary dissociation constant ADP
$K_{id, Mi}$	1.5977	mM	binary dissociation constant PCr
$K_{b, Mi}$	5.209	mM	ternary dissociation constant Cr
$K_{d, Mi}$	4.99E-1	mM	ternary dissociation constant PCr
$K_{c, Mi}$	$K_{ic, Mi}$$K_{d, Mi}$/$K_{id, Mi}$	mM	ternary dissociation constant ADP
$K_{Ib, Mi}$	$K_{ib, Mi}$	mM	ternary dissociation constant Cr from dead end complex
$C_{CK, Mi}$			mitochondrial creatine kinase activity
MMCK			cytosol creatine kinase enzyme (MiCK activity is about 15% of the total CK activity in heart)
$V_{max,MM,f}$	6.996E-3	mM/ms	maximum velocity in the forward direction (PCr production)
$V_{max,MM,b}$	calculated	mM/ms	maximum velocity in the backward direction (ATP production)
$K_{ia, MM}$	9E-1	mM	binary dissociation constant ATP
$K_{ib, MM}$	1.55E1	mM	binary dissociation constant Cr
$K_{ic, MM}$	2.224E-1	mM	binary dissociation constant ADP
$K_{id, MM}$	1.670	mM	binary dissociation constant PCr
$K_{b, MM}$	3.49E1	mM	ternary dissociation constant Cr
$K_{d, MM}$	4.73	mM	ternary dissociation constant PCr
$K_{c, MM}$	$K_{ic, Mi}$$K_{d, Mi}$/$K_{id, Mi}$	mM	ternary dissociation constant ADP
$K_{Ib, MM}$	$K_{ib, Mi}$	mM	ternary dissociation constant Cr from dead end complex
$C_{CK, MM}$			cytosol creatine kinase activity
Permeability
$R_{ATP}$	8.16	Hz	diffusional conductance ATP
$R_{ADP}$	65.2227	Hz	diffusional conductance ADP
$R_{PCr}$	24615	Hz	diffusional conductance PCr
$R_{Cr}$	1166.7	Hz	diffusional conductance Cr
$R_{Pi}$	6.0318	Hz	diffusional conductance Pi
$V_{cyto}$	3		Fractional volume of cytosol. Total volume 1 corresponds to $V_{mito}$=0.153mL/gww.
$V_{ims}$	1/4		Fractional volume of intermembrane space.

Footnotes

1. Kongas O, van Beek JHGM Creatine kinase in energy metabolic signaling in muscle Nature Precedings (2007)DOI: https://doi.org/10.1038/npre.2007.1317.1 ↩